Question

If there were 64 sixth graders, list all of the ways they could have been divided equally into groups of 10 or fewer students?

Answer 1

There are four ways in which sixth graders could have been divided equally into groups of `10` or fewer students.

Explanation:

We have `64` sixth graders. Let us write the group sizes of `10` or fewer size in which they can be divided equally starting from `1` in increasing order in a column (these will be obviously factors of `64`) and then against them, let us write the number of groups.

The result is as follows:

`Number` `of` `groupscolor(white)(XXXXXX)Group` `Size`

`color(white)(XX)1color(white)(XXXXXXXXXXXXXXX)64`
`color(white)(XX)2color(white)(XXXXXXXXXXXXXXX)32`
`color(white)(XX)4color(white)(XXXXXXXXXXXXXXX)16`
`color(white)(XX)8color(white)(XXXXXXXXXxxXXXXX)8`

As next number can only be `16`, which is greater than `0`, we stop here. Hence

There are four ways in which sixth graders could have been divided equally into groups of `10` or fewer students.